Question 1

The annual return of a well-known mutual fund has historically had a mean of about 10% and a standard deviation of 21%. Suppose the return for the following year follows a normal distribution, with the historical mean and standard deviation. What is the probability that you will lose money in the next year by investing in this fund?

Accepted Answer

The answer of The annual return of a well-known mutual...

Question 2

The average annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5% (Inflationdata.com). In 1980, the inflation rate was above 13%. If the annual inflation rate is normally distributed, what is the probability that inflation will be above 13% next year?

Accepted Answer

The answer of The average annual inflation rate in the...

Question 3

The Japan Sumo Association has begun to measure the body fat of wrestlers to try to combat the growing problem of excessive obesity within the sport. As of last year, the average wrestler weighed 412 pounds. Suppose the weights of sumo wrestlers are normally distributed, with a standard deviation of 37 pounds. What is the probability that a randomly selected wrestler weighs between 350 and 450 pounds?

Accepted Answer

The answer of The Japan Sumo Association has begun to...

Question 4

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 9%, with a standard deviation of 12%. The relatively less risky fund promises an expected return and standard deviation of 5% and 8%, respectively.
A) Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return?
B) Which mutual fund will you pick if your objective is to maximize the probability of earning a return of between 8% and 12%?

Accepted Answer

The answer of You are considering the risk-return profile of...

Question 5

Jennifer is waiting for a taxicab. The average wait time for a taxi is six minutes. Suppose the wait time is exponentially distributed. What is the probability that a taxi arrives in three minutes or less?

Accepted Answer

The answer of Jennifer is waiting for a taxicab. The...

Question 6

A normal random variable X has a mean of 17 and a variance of 5.
A) Find the value x for which P(X ≤ x) = 0.0020.
B) Find the value of x for which P(X > x) = 0.0122.

Accepted Answer

The answer of A normal random variable X has a...

Question 7

Let the household income of residents of the United States be represented by Y = e^X, where X is normally distributed. Last year, the mean U.S. household income was approximately $50,000. Suppose the standard deviation was 16,000. Estimate the proportion of U.S. households that have an income less than 80,000.

Accepted Answer

The answer of Let the household income of residents of...

Question 8

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 2; σ² = 1.8.

Accepted Answer

The answer of Compute the mean and variance of a...

Question 9

After a heavy snow, the city of Boston spends millions of dollars plowing the streets. Suppose the amount of time the city must spend before the streets are clear follows a log-normal distribution. Further suppose that the average amount of time is 12 hours and the standard deviation is 5 hours. What percentage of the time does it take more than 10 hours for the streets to be cleared?

Accepted Answer

The answer of After a heavy snow, the city of...

Question 10

The average wait time to see a doctor at a maternity ward is 16 minutes. What is the probability that a patient will have to wait between 20 and 30 minutes before seeing a doctor? Suppose the wait time is exponentially distributed.

Accepted Answer

The answer of The average wait time to see a...

Question 11

The East Los Angeles Interchange is the busiest freeway interchange in the world. Last year, an average of 550,000 cars passed through the intersection per day with a standard deviation of 100,000. What is the probability more than 620,000 use the interchange on a random day? Assume the number of cars on the interchange is approximately normally distributed.

Accepted Answer

The answer of The East Los Angeles Interchange is the...

Question 12

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4, find the following probabilities.
A) P(11 < X ≤ 16.4)
B) P(9 ≤ X < 11.5)
C) P(8.6 < X < 15.4)
D) P(X > 13.6)

Accepted Answer

The answer of Given normally distributed random variable X with...

Question 13

A soft drink company fills two-liter bottles on several different lines of production equipment. The fill volumes are normally distributed with a mean of 1.97 liters and a variance of 0.04 (liter)². A) Find the probability that a randomly selected two-liter bottle would contain more than 1.92 liters. B) If X is the fill volume of a randomly selected two-liter bottle, find the value of x for which P(X < x) = 0.6293.

Accepted Answer

The answer of A soft drink company fills two-liter bottles...

Question 14

Suppose the amount of time customers must wait to check bags at the ticketing counter in Boston Logan Airport is exponentially distributed with a mean of 14 minutes. What is the probability that a randomly selected customer will have to wait more than 20 minutes?

Accepted Answer

The answer of Suppose the amount of time customers must...

Question 15

A producer has a history of making bad movies. The movies he has produced have averaged $160,000 dollars at the box office with a standard deviation of $185,000. He thinks his latest movie will be a huge hit. How much will the movie earn at the box office if it is only expected to earn that much or more 0.5% of the time? (Assume that the profit at the box office is normally distributed.)

Accepted Answer

The answer of A producer has a history of making...

Question 16

Customers arrive at a drive-through teller window of a bank. They stay in line when the teller is busy. The service time is exponentially distributed with a mean of four minutes.
A) What is the probability that the next customer in line will take longer than seven minutes to be served?
B) What is the probability that the next customer in line will take less than eight minutes to be served?
C) What is the probability that the next customer in line will take between three and six minutes to be served?

Accepted Answer

The answer of Customers arrive at a drive-through teller window...

Question 17

The average annual percentage rate (APR) for credit cards held by U.S. consumers is approximately 15 percent ("Ouch - Credit Card APR Now Tops 15 Percent," Time, January 3, 2012). Suppose the APR for new credit card offers is normally distributed with a mean of 15% and a standard deviation of 4%. What APR must a credit card charge to be in the bottom 10% of all cards?

Accepted Answer

The answer of The average annual percentage rate (APR) for...

Question 18

The weight of competition pumpkins at the Circleville Pumpkin Show in Circleville, Ohio, can be represented by a normal distribution with a mean of 703 pounds and a standard deviation of 347 pounds.
A) Find the probability that a randomly selected pumpkin weighs at least 1,622 pounds.
B) Find the probability that a randomly selected pumpkin weighs between 465.1 and 1,622 pounds.

Accepted Answer

The answer of The weight of competition pumpkins at the...

Question 19

The average wait time at a McDonald's drive-through window is about three minutes ("The Doctor Will See You Eventually," The Wall Street Journal, October 18, 2010). Suppose the wait time is exponentially distributed. What is the probability that a randomly selected customer will have to wait no more than five minutes?

Accepted Answer

The answer of The average wait time at a McDonald's...

Question 20

A soft drink company fills two-liter bottles on several different lines of production equipment. The fill volumes are normally distributed with a mean of 1.97 liters and a variance of 0.04 (liter)². A) Find the probability that a randomly selected two-liter bottle would contain between 1.95 and 2.03 liters. B) If X is the fill volume of a randomly selected two-liter bottle, find the value of x for which P(X > x) = 0.3228.

Accepted Answer

The answer of A soft drink company fills two-liter bottles...

Quiz 6: Continuous Probability Distributions

Jennifer is waiting for a taxicab. The average wait time for a taxi is six minutes. Suppose the wait time is exponentially distributed. What is the probability that a taxi arrives in three minutes or less?

A normal random variable X has a mean of 17 and a variance of 5. A) Find the value x for which P(X ≤ x) = 0.0020. B) Find the value of x for which P(X > x) = 0.0122.

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 2; σ2 = 1.8.

The average wait time to see a doctor at a maternity ward is 16 minutes. What is the probability that a patient will have to wait between 20 and 30 minutes before seeing a doctor? Suppose the wait time is exponentially distributed.

Given normally distributed random variable X with a mean of 12 and a standard deviation of 3.4, find the following probabilities. A) P(11 < X ≤ 16.4) B) P(9 ≤ X < 11.5) C) P(8.6 < X < 15.4) D) P(X > 13.6)

Suppose the amount of time customers must wait to check bags at the ticketing counter in Boston Logan Airport is exponentially distributed with a mean of 14 minutes. What is the probability that a randomly selected customer will have to wait more than 20 minutes?

Compute the mean and variance of a lognormal variable Y if the mean and the variance of the underlying normal variable are μ = 2; σ² = 1.8.